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Pereverzev A, Sewell TD. Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX. J Chem Phys. 2015;142(13):134110doi: 10.1063/1.4916614.
Pereverzev, A., & Sewell, T. D. (2015). Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX. The Journal of chemical physics, 142(13), 134110. https://doi.org/10.1063/1.4916614
Pereverzev, Andrey, and Sewell, Thomas D. "Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX." The Journal of chemical physics vol. 142,13 (2015): 134110. doi: https://doi.org/10.1063/1.4916614
Pereverzev A, Sewell TD. Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX. J Chem Phys. 2015 Apr 07;142(13):134110. doi: 10.1063/1.4916614. PMID: 25854231.
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J Chem Phys. 2015 Apr 07;142(13):134110. doi: 10.1063/1.4916614.

Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX.

The Journal of chemical physics

Andrey Pereverzev, Thomas D Sewell

Affiliations

  1. Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211-7600, USA.

PMID: 25854231 DOI: 10.1063/1.4916614

Abstract

We show that for solids the effective Hessian matrix, averaged over the canonical ensemble, can be calculated from the force covariance matrix. This effective Hessian reduces to the standard Hessian as the temperature approaches zero, while at finite temperatures it implicitly includes anharmonic corrections. As a case study, we calculate the effective Hessians and the corresponding normal mode eigenvectors and frequencies for the crystalline organic explosives pentaerythritol tetranitrate and α-1,3,5-trinitro-1,3,5-triazacyclohexane. The resulting normal mode frequencies are compared to those obtained by diagonalizing the standard Hessian matrix of second derivatives in Cartesian displacements about the potential energy minimum. Effects of temperature and statistical noise on the effective Hessians and normal mode frequencies are discussed.

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